CF1157E.Minimum Array

You are given two arrays $a$ and $b$ , both of length $n$ . All elements of both arrays are from $0$ to $n-1$ .

You can reorder elements of the array $b$ (if you want, you may leave the order of elements as it is). After that, let array $c$ be the array of length $n$ , the $i$ -th element of this array is $c_i = (a_i + b_i) \% n$ , where $x \% y$ is $x$ modulo $y$ .

Your task is to reorder elements of the array $b$ to obtain the lexicographically minimum possible array $c$ .

Array $x$ of length $n$ is lexicographically less than array $y$ of length $n$ , if there exists such $i$ ( $1 \le i \le n$ ), that $x_i < y_i$ , and for any $j$ ( $1 \le j < i$ ) $x_j = y_j$ .

The first line of the input contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of elements in $a$ , $b$ and $c$ .

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i < n$ ), where $a_i$ is the $i$ -th element of $a$ .

The third line of the input contains $n$ integers $b_1, b_2, \dots, b_n$ ( $0 \le b_i < n$ ), where $b_i$ is the $i$ -th element of $b$ .

Print the lexicographically minimum possible array $c$ . Recall that your task is to reorder elements of the array $b$ and obtain the lexicographically minimum possible array $c$ , where the $i$ -th element of $c$ is $c_i = (a_i + b_i) \% n$ .